Nano-Scale and Atomistic-Scale Modeling of Advanced Materials

The studies on advanced materials at sub-micron scales have become a popular subject in engineering sciences and technology development in the past decade. In general, experimental investigations at this scale are very difficult and may be unreliable. Therefore, analytical and computational modeling appears to be rather critical and important in such studies. The objective of this chapter is to review two state-of-the-arts approaches for modeling advanced materials at the nano- and the atomistic scales, respectively.

The first part of this chapter introduces a unit cell model for the analysis of composites with carbon nanotubes (CNTs) and epoxy resin using finite element method (FEM). Varying CNT orientation is considered in order to describe the behaviors of the randomly oriented CNTs inside the epoxy matrix. Composite loss factors are calculated based on the average ratio of the unit cell energy loss to the unit cell energy input. Calculated loss factors under different strain levels are compared to experimental data. With the validated model, parametric study is thereafter performed. Parameters such as CNT dimension and CNT alignment orientation are studied. Those factors lead to higher composite damping capacity are identified.

The second part of this chapter proposes a novel atomistic–continuum mechanics which is a hybrid method for coupling continuum mechanics and interatomic potential function to predict the mechanical behavior of nano-scale single crystal silicon under uniaxial tensile loading. The atomistic–continuum mechanics is based on the transformation of chemical bonds between atoms in molecular mechanics into appropriate elements in finite element method and continuum mechanics. There are many methods used in nano-structure analysis such as molecular dynamics (MD) and ab initio calculation; the molecular dynamics simulation is one of the most promising methods for investigating the mechanical properties of structure and material at nano-scale. However, it requires extensive computing time and cost. Furthermore, in traditional continuum mechanics, the finite element method (FEM) is widely used to model and simulate the mechanical behaviors of solid/discrete body; it is a mature technology after decades of development. Compared with MD simulation, the continuum mechanics can be very efficient as it can provide results quickly in an accurate range. In the hybrid approach, the total energy of the nano-structure is formed by each individual potential energy of bi-atom, once the total potential is assembled the FEM could take the minimization of the total energy, which includes the potential energy and external works, and to solve the structure by conventional way. Therefore, this study employs FEM to explore the mechanical properties of nano-scale single crystal silicon. This research also utilizes an interatomic potential function to describe the interaction of each atom. A general form of Stillinger–Weber potential function was used for interaction between the silicon atoms in the simulations. Based on atomistic–continuum simulation results, the Young’s modulus of single crystal silicon in various crystallographic planes could be estimated. The results obtained from the present modeling approach are in reasonable agreement with the experiment and simulation results reported in the literature.